# Minimum sum of two numbers formed from digits of an array in O(n)

Given an array of digits (values are from 0 to 9), find the minimum possible sum of two numbers formed from digits of the array. All digits of the given array must be used to form the two numbers.

Examples:

Input: arr[] = {6, 8, 4, 5, 2, 3}
Output: 604
246 + 358 = 604

Input: arr[] = {5, 3, 0, 7, 4}
Output: 82

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: A minimum number will be formed from the set of digits when smallest digit appears at the most significant position and next to smallest digit appears at next most significant position and so on…

The idea is to build two numbers by alternating picking digits from the array (assuming it is sorted in ascending). So the first number is formed by digits present in odd positions in the array and the second number is formed by digits from even positions in the array. Finally, we return the sum of the first and second number. In order to reduce the time complexity, the array can be sorted in O(n) using the frequency array of digits as every element of the original array is a single digit i.e. there can be at most 10 distinct elements.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the required minimum sum  ` `int` `minSum(vector<``int``> arr, ``int` `n)  ` `{  ` ` `  `    ``// Array to store the  ` `    ``// frequency of each digit  ` `    ``int` `MAX = 10; ` `    ``int` `*freq = ``new` `int``[MAX];  ` `    ``for` `(``int` `i = 0; i < n; i++) {  ` ` `  `        ``// Store count of every digit  ` `        ``freq[arr[i]]++;  ` `    ``}  ` ` `  `    ``// Update arr[] such that it is  ` `    ``// sorted in ascending  ` `    ``int` `k = 0;  ` `    ``for` `(``int` `i = 0; i < MAX; i++) {  ` ` `  `        ``// Adding elements in arr[]  ` `        ``// in sorted order  ` `        ``for` `(``int` `j = 0; j < freq[i]; j++) {  ` `            ``arr[k++] = i;  ` `        ``}  ` `    ``}  ` ` `  `    ``int` `num1 = 0;  ` `    ``int` `num2 = 0;  ` ` `  `    ``// Generating numbers alternatively  ` `    ``for` `(``int` `i = 0; i < n; i++) {  ` ` `  `        ``if` `(i % 2 == 0)  ` `            ``num1 = num1 * MAX + arr[i];  ` `        ``else` `            ``num2 = num2 * MAX + arr[i];  ` `    ``}  ` ` `  `    ``// Return the minimum possible sum  ` `    ``return` `num1 + num2;  ` `}  ` ` `  `// Driver code  ` `int` `main(``void``)  ` `{  ` `    ``vector<``int``>arr = { 6, 8, 4, 5, 2, 3 };  ` `    ``int` `n = arr.size();  ` `    ``cout << minSum(arr, n);  ` `}  ` `// This code is contributed by ankush_953 `

## Java

 `// Java implementation of above approach ` `public` `class` `GFG { ` ` `  `    ``public` `static` `final` `int` `MAX = ``10``; ` ` `  `    ``// Function to return the required minimum sum ` `    ``static` `int` `minSum(``int` `arr[], ``int` `n) ` `    ``{ ` ` `  `        ``// Array to store the ` `        ``// frequency of each digit ` `        ``int` `freq[] = ``new` `int``[MAX]; ` `        ``for` `(``int` `i = ``0``; i < n; i++) { ` ` `  `            ``// Store count of every digit ` `            ``freq[arr[i]]++; ` `        ``} ` ` `  `        ``// Update arr[] such that it is ` `        ``// sorted in ascending ` `        ``int` `k = ``0``; ` `        ``for` `(``int` `i = ``0``; i < MAX; i++) { ` ` `  `            ``// Adding elements in arr[] ` `            ``// in sorted order ` `            ``for` `(``int` `j = ``0``; j < freq[i]; j++) { ` `                ``arr[k++] = i; ` `            ``} ` `        ``} ` ` `  `        ``int` `num1 = ``0``; ` `        ``int` `num2 = ``0``; ` ` `  `        ``// Generating numbers alternatively ` `        ``for` `(``int` `i = ``0``; i < n; i++) { ` ` `  `            ``if` `(i % ``2` `== ``0``) ` `                ``num1 = num1 * MAX + arr[i]; ` `            ``else` `                ``num2 = num2 * MAX + arr[i]; ` `        ``} ` ` `  `        ``// Return the minimum possible sum ` `        ``return` `num1 + num2; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = { ``6``, ``8``, ``4``, ``5``, ``2``, ``3` `}; ` `        ``int` `n = arr.length; ` `        ``System.out.print(minSum(arr, n)); ` `    ``} ` `} `

## Python3

 `# Python implementation of above approach ` `# Function to return the required minimum sum  ` `def` `minSum(arr, n): ` `    ``# Array to store the  ` `    ``# frequency of each digit  ` `    ``MAX` `=` `10` `    ``freq ``=` `[``0``]``*``MAX` `     `  `    ``for` `i ``in` `range``(n): ` `        ``# Store count of every digit  ` `        ``freq[arr[i]] ``+``=` `1` ` `  `    ``# Update arr[] such that it is  ` `    ``# sorted in ascending  ` `    ``k ``=` `0` `    ``for` `i ``in` `range``(``MAX``): ` `        ``# Adding elements in arr[]  ` `        ``# in sorted order  ` `        ``for` `j ``in` `range``(``0``,freq[i]):  ` `            ``arr[k] ``=` `i ` `            ``k ``+``=` `1` ` `  `    ``num1 ``=` `0` `    ``num2 ``=` `0` ` `  `    ``# Generating numbers alternatively  ` `    ``for` `i ``in` `range``(n): ` `        ``if` `i ``%` `2` `=``=` `0``: ` `            ``num1 ``=` `num1 ``*` `MAX` `+` `arr[i] ` `        ``else``: ` `            ``num2 ``=` `num2 ``*` `MAX` `+` `arr[i]  ` ` `  `    ``# Return the minimum possible sum  ` `    ``return` `num1 ``+` `num2  ` ` `  ` `  `# Driver code  ` `arr ``=` `[ ``6``, ``8``, ``4``, ``5``, ``2``, ``3` `] ` `n ``=` `len``(arr);  ` `print``(minSum(arr, n)) ` ` `  `#This code is contributed by ankush_953 `

## C#

 `// C# implementation of above approach ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``public` `static` `int` `MAX = 10; ` `    ``// Function to return the required minimum sum ` `    ``static` `int` `minSum(``int``[] arr, ``int` `n) ` `    ``{ ` ` `  `        ``// Array to store the ` `        ``// frequency of each digit ` `        ``int``[] freq = ``new` `int``[MAX]; ` `        ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `            ``// Store count of every digit ` `            ``freq[arr[i]]++; ` `        ``} ` ` `  `        ``// Update arr[] such that it is ` `        ``// sorted in ascending ` `        ``int` `k = 0; ` `        ``for` `(``int` `i = 0; i < MAX; i++) { ` ` `  `            ``// Adding elements in arr[] ` `            ``// in sorted order ` `            ``for` `(``int` `j = 0; j < freq[i]; j++) { ` `                ``arr[k++] = i; ` `            ``} ` `        ``} ` ` `  `        ``int` `num1 = 0; ` `        ``int` `num2 = 0; ` ` `  `        ``// Generating numbers alternatively ` `        ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `            ``if` `(i % 2 == 0) ` `                ``num1 = num1 * MAX + arr[i]; ` `            ``else` `                ``num2 = num2 * MAX + arr[i]; ` `        ``} ` ` `  `        ``// Return the minimum possible sum ` `        ``return` `num1 + num2; ` `    ``} ` ` `  `    ``// Driver code ` `    ``static` `public` `void` `Main() ` `    ``{ ` `        ``int``[] arr = { 6, 8, 4, 5, 2, 3 }; ` `        ``int` `n = arr.Length; ` `        ``Console.WriteLine(minSum(arr, n)); ` `    ``} ` `} ` ` `  `// This code is contributed by jit_t. `

Output:

```604
```

Time Complexity: O(n)

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : jit_t, ankush_953

Article Tags :
Practice Tags :

4

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.